Pressley guided the Bairns to victory over Aberdeen amid three defeats against top-six opposition but Falkirk host St Johnstone on Saturday in the first of several games against teams just above them in the table.
Falkirk face Hamilton, St Mirren and the Perth side again before the SPL splits and Twaddle knows they need to pick up points.
"Performances have been there but obviously results haven't but now we are playing a lot of teams round about us with Hamilton and St Mirren coming up as well, this is the time to start picking up points," he said.
"We looked really good against Celtic but you don't pay £65,000 a week for nothing.
"There were two great finishes from Robbie Keane but apart from that I think we controlled the game.
"We were gutted on Sunday but we just need to move on and stay positive. If we play like that, I think we'll win more than we lose.
"We created a lot of good chances against a good Celtic side, I think we had 11 shots to their five so that shows how the game went.
"I think one day all of these chances are going to go in."
Twaddle's confidence mirrors the attitude of Pressley, who assured Falkirk fans the team would stay up when he took over last month.
"Elvis is a positive guy as you have seen in his press and we're the same, we're positive players," the former Partick Thistle player said.
"Our aim is to stay in this league. He gives the players confidence, him and Alex (Smith) have done a great job with Bully (Lee Bullen) as well. They rub off on each other and the players have responded well."
Falkirk lost 3-1 at McDiarmid Park earlier this season and Twaddle is expecting a busy day defensively, but he believes his team have plenty of reason for optimism.
"They are a good side and they are a strong team," the 23-year-old said. "I played against them last year a number of times with Thistle. They are physical and like to attack, they have scored a lot of goals this year.
"But we think we're a good team and we can create chances. We hope we can take a few this time instead of missing them."
Source: Team Talk